Final answer:
The simplified forms are (a) -2x + 7, combining like terms; (b) 3x + 29, after subtracting expressions and combining like terms; and (c) 28x^2 - 63x, by distributing and multiplying terms.
Step-by-step explanation:
To simplify the given expressions, we need to combine like terms and apply the rules for addition, subtraction, and multiplication of numbers with different signs.
(a) Simplifying the sum of 6x + 2 and -8x + 5
We combine like terms (terms with the same variable and exponent) and constant terms:
6x + 2 + (-8x) + 5 = (6x - 8x) + (2 + 5) = -2x + 7
(b) Simplifying the result of subtracting 5x - 17 from 8x + 12
To subtract one expression from another, we change the signs of the terms being subtracted and then combine like terms:
(8x + 12) - (5x - 17) = 8x + 12 - 5x + 17 = (8x - 5x) + (12 + 17) = 3x + 29
(c) Simplifying the product of 7x and 4x - 9
We distribute the 7x across the terms of the second expression:
7x * (4x - 9) = (7x * 4x) - (7x * 9) = 28x^2 - 63x